Method and apparatus for electromagnetic emissions testing

ABSTRACT

The likelihood of a system complying with EMC regulations is determined for a system comprised equipment units which individually radiate electromagnetic emissions. The intensity contribution of the electric field from each of the equipment units is calculated and a phase difference is randomly assigned to each of the components repeatedly in order to generate distribution of electric field values between a minium possible electric field value and a maximum possible electric field value. This distribution is then statistically analysed to determine a compliance probability.

The present invention generally relates to the field of electromagneticemissions testing. In particular the present invention relates to amethod and apparatus for determining the likelihood of an electric fieldat a position and caused by electromagnetic emissions from a system adistance from the position being less than or more than a predefinedelectric field, where the system comprises a plurality of equipmentunits each of which individually radiate electromagnetic emissions.

There is a requirement for modern electrical and electronic equipment tomeet a series of mandatory electromagnetic compatibility (EMC)requirements. One of the requirements is for the radiatedelectromagnetic emissions to be below a certain level in order to avoidinterference to adjacent users of the radio frequency spectrum and otheradjacent electrical and electronic equipment.

Certain electrical or electronic equipment is capable of being placed ona test facility whereupon the radiated electromagnetic emissions can bemeasured directly. Typically measurements are made at 3, 10, and 30metres distance and the electronic fields at these distances aremeasured for vertical and horizontal polarities and for variousradiation frequencies. The EMC regulations such as the European Union(EU) Directive 89/336/EEC which came into force on Jan. 1, 1996 setsfield levels which must be met by both individual equipment units andsystems comprising a plurality of equipment units.

Demonstrating compliance of equipment units is the responsibility of thebody that makes the unit available for sale within the European market(either the manufacturer or the importer). Demonstrating the complianceof systems is the responsibility of the Systems Integretor or that bodyon whose behalf the system is bought into operation.

Whilst it is possible to place some equipment on a test facility andmeasure emissions whilst the equipment is operated, for larger systemsand installations this may not just be impractical but also impossible.For example, the testing of the radiated emissions for a telephoneexchange would require the complete telephone exchange to be placed on atest facility and it would be necessary to simulate typical operation ofthe exchange.

For this reason it is also possible in order to demonstrate compliancewith the EMC regulations to generate what are termed TechnicalConstruction Files (TCFs) for each system or installation. Under theterms of the EU Directive a TCF records all information relevant to theEMC performance of the item it concerns.

Using TCFs it is possible to demonstrate compliance with the EMCregulations by predicting the electromagnetic compatibility of theequipment and the present invention is concerned with a particularmethod of prediction that leasds the system owner to conflude that itcomplies with the protection requirements of the regulations.

In accordance with an aspect of the present invention there is provideda method of determining electromagnetic compatibility by predicting thelikelihood of compliance with the radiated emissions standards. This isachieved by calculating the contribution to the electromagnetic fieldcaused by emissions from equipment units forming the system andassigning a random relative phase to the components in order to build upa distribution of possible electromagnetic field values. Thisdistribution can then be statistically analysed to determine thelikelihood of compliance.

Thus for systems and installations which are comprised of large numbersof equipment units, the present inventor has realised that it is inprinciple possible to consider the field emitted from the systemresulting from the combination of the emissions from the equipmentunits, if the following is known for each equipment unit: (I) theindividually radiated electric field at the point of interest; (ii) therelative phase of the individually radiated electric fields at the pointof interest. However, the relative phase of the emissions from theequipment units can not be accurately predicted. The inventor hasovercome this problem by using a statistical technique whereby therelative phase of each contribution is randomised in order to determinea statistical distribution for the field emitted by the system. Fromthis statistical distribution the likelihood of compliance with thestandard can then be determined.

In one particular embodiment this statistical analysis techniquecomprises determining the cumulative probability for the electric fieldvalues and determining if, for the electric field threshold defined bythe standard, the cumulative probability is above or below thethreshold.

The statistical technique used in the present invention is considered tobe a particularly valid one in view of the variability of emissions ofthe equipment due to both operating variations and manufacturingvariations. In particular, in a publication The International SpecialCommittee on Radio Interference, CISPR 22, 3rd Edition 1997-11, Section7, Interpretation of CISPR Radio Distribution Limit, Sub-Section 7.1.2it is stated “The significance of the limits for equipment shall bethat, on a statistical basis, at least 80% of the mass producedequipment complies with the limits with at least 80% confidence”.

In an embodiment of the present invention the relative phase is randomlyselected in accordance with a predefined probability distribution ofpossible relative phases. Preferably, each possible relative phase hasequal probability in the predefined probability distribution.

The individual electric field components generated by individualequipment units can be calculated based on the distances from theequipment units to the defined position and based on knownelectromagnetic emission properties of the equipment units. Such a knownelectromagnetic emission properties can either comprise a measuredelectric field at a distance from the equipment unit, or can beinformation which is provided with the equipment unit.

The electromagnetic emission from the units can be emitted at aplurality of frequencies and at various polarities. The method ofdetermining the likelihood of compliance of the system with the standardcan include determining the likelihood for each frequency and polaritye.g. vertical and horizontal polarities.

In an embodiment of the present invention the minimum possible compoundelectric field is determined using the individually calculatedelectrical field components and if the minimum possible compoundelectric field is greater than the predefined electric field, clearlythe system cannot meet the standard and the statistical analysis is notcarried.

The maximum possible compound electric field is determined using theindividual calculated electric field components and if the maximumpossible compound electric field is not greater than the predefinedelectric field, clearly the system cannot fail the standard and thus thestatistical analysis need not be carried out. If the maximum possiblecompound electric field and the minimum possible compound electric fieldis less than the predefined electric field, is greater than thepredefined electric field, the likelihood of the equipment complyingwith the standards must be determined.

Using the technique of the present invention, in an embodiment of thepresent invention it is possible to map around the system to provide“contours” of EMC compliance probability. This mapping may be importantfor example which considering an installation and its effect on itsneighbours. For example, there may be highly sensitive equipment in theneighbourhood in one direction and thus in this direction the emissionswill need to be reduced.

Using the method of the present invention it is thus possible to designa system which comprises a plurality of equipment units. Units can bearranged in dependence upon their emissions in order to meet the desiredemission criteria. Such a method can be implemented on a computer toprovide a graphical user interface allowing the user to move the unitsabout within the model of the equipment.

The present invention can be implemented as a computer program operatingon a standard computer and thus one aspect of the present inventionprovides a storage medium containing processor implementableinstructions for controlling a processor to carry out the method.Another aspect of the present invention provides an electronic signalcarrying computer code for instructing a processor to carry out themethod.

Embodiments of the present invention will now be described withreference to the accompanying drawings in which:

FIG. 1 is a graph showing the CISPR 22: 1997 radiated field limits forinformation technology equipment (ITE)

FIG. 2 schematically illustrates the contribution to the compoundelectric field from equipment units forming a system such as a largeinstallation;

FIG. 3 is a graph illustrating the random probability density for thephase differences;

FIG. 4 is an Argand diagram illustrating the combination of electricfield components;

FIGS. 5a and 5 b are a flow diagram illustrating the method of anembodiment of the present invention;

FIG. 6 is a graph showing the calculated probability distribution forelectric field emitted by a complex system such as an installation;

FIG. 7 is a graph illustrating the cumulative probability derived fromthe probability distribution in FIG. 6;

FIG. 8 is a functional diagram of apparatus in accordance with anembodiment of the present invention; and

FIG. 9 is a schematic diagram of a design system incorporating theapparatus of FIG. 8 in accordance with an embodiment to the presentinvention.

Referring to the drawings, FIG. 1 illustrates the CISPR 22: 1997emissions limits in the frequency range 30 MHz to 1 GHz for class Aequipment (industrial) environment and class B equipment (domestic lightindustrial) environment when measured at 10 metres from the equipment.FIG. 2 schematically illustrates a complex system such as a telephoneexchange which comprises a number of equipment units which form sourcesS1 to S5 of electromagnetic emission e.g. switches. In order to meet theEMC regulations, at a specific distance such as 10 metres (indicated bythe dotted line 1 in FIG. 2), the combined effect of the emissions ofall of the sources S1 to S5 must be below the required levels. Thus asshown in FIG. 2 at an analysis point (AP) on the boundary 1 the combinedeffect of the emissions of the sources S1 to S5 must be determined.

Since for practical reasons in many instances these cannot be measured.The inventors have applied a method of predicting the resultant field.

The emissions of the equipment units forming the system 2 can bedetermined either for example by direct measurement, or from theinformation given by the manufacturers and/or suppliers. Thisinformation can give complete information for emissions over a range offrequencies and at different polarities. This information is usuallyrequired in order for the manufacturers and/or suppliers of theequipment units to themselves meet the EMC regulations.

Although information is thus available on electromagnetic emissions fromthe equipment units, in order for the resultant electric field at theanalysis point (AP) to be calculated it is necessary to know both theintensity and phase of the electric field components contributing to theresultant field. There are two factors which effect these:

1. propagation distances; and

2. synchrocinity of generation of the electromagnetic emissions.

The propagation distances effect both the intensity and phase of theelectromagnetic emission and the usual inverse rule can be used todetermine the propagation loss and thus the intensity at the analysispoint. Also, the propagation distances could be used to calculate thephase differences caused by propagation distances if the initial phaseof the generated electromagnetic emission was known. However, thesynchrocinity of generation can be extremely difficult, if at allpossible, to derive since this can be varied both by thermal drift andby variations in switching for example in the equipment units.

Thus although the intensity of the electric field at a distance from thesource can be determined from the equation below, the phase of theelectric field s indeterminable.$E_{2} = {E_{1} + {20 \cdot {\log_{10}\left\lbrack \frac{r_{1}}{r_{2}} \right\rbrack}}}$

where E₁ is the electric field intensity measured at a distance r₁ fromthe source, and E₂ is the electric field intensity measured at adistance r₂ from the source.

If the worst case scenario is considered and all of the sources emitsuch that the emissions are in phase as they emit at the analysis point,then the electric field at the analysis point is simply given by summingthe electric field components due to electromagnetic emissions from thesources S1 to S5. If this worst case electric field value is below thethreshold electric field defined in the EMC standard, then clearly theequipment 2 can never fail the EMC standard. In this case the equipment2 is 100% compliant with the EMC standard. If however, the maximumpossible field at the analysis point exceeds the threshold field set bythe standard, it is necessary to take into consideration the phase inorder to be able to give a probability that the system will comply withthe standard.

In the present invention the phase difference between each source isassumed to be unknown. A phase difference having a random probabilitydistribution is used for assigning the phase difference between theemissions of the sources. Given that a random variable is able andequally likely to adopt any value within its specified, a random phasedifference has a probability distribution as illustrated in FIG. 3. Ascan be seen in FIG. 3 the probability of a sources phase differenceadopting any value is ½ π. To evaluate the combined electric fieldintensity at the analysis point, one of the emissions (generally thelargest emission) is selected as the phase reference. Further emissionsare free to adopt any phase difference with respect of this referenceand are therefore referred to as “independent”.

FIG. 4 illustrates the calculation of the peak amplitude of the combinedfield values and comprises an Argand Diagram. In this diagram thereference phase field is given by E₁, the phase independent field isgiven by E₂ and the resultant field is given by E_(c).

The peak amplitude of the combined field E_(c) is given by Pythagorusas:

E _(c)={square root over ((E _(r) ² +E _(i) ²))}

where

E _(r) =E ₁ +E ₂ cos φ

E _(i) =E ₂ sin φ

where E_(r) and E_(i) are the real and imaginary components peakamplitude of the combined field respectively.

FIGS. 5a and 5 b are a flow diagram illustrating the steps performed bythe method in order to determine the compliance probability.

In step S1 the emission data for the equipment units of the system isinput and in step S2 the analysis point is selected. The electric fieldvalues E_(n) at the analysis point for the n equipment units are thencalculated in step S3 and these are then ordered in descending order ofmagnitude (S4).

Hence

 E ₁ ≧E ₂ ≧ . . . ≧E _(n−1) ≧E _(n)

The maximum possible peak amplitude of the combined field at theanalysis point is then determined in step S5 using:$E_{\max} = {\sum\limits_{n}\quad E_{n}}$

Thus, the maximum possible electric field is merely the sum of all ofthe electric field components assuming that all are in the phase andconstructively add.

In step S6 it is determined whether the maximum possible electric fieldis less than or equal to the threshold i.e. E_(max)≦E_(limit). If so instep S7 the compliance probability is set to 1 and the process proceedsto step S21 to output the compliance probability.

If E_(max)>E_(limit), in step S8 the minimum combined electric fieldE_(min) is then determined using:$E_{\min} = {{{\left( {E_{r} - {\sum\limits_{n}\quad E_{n}}} \right){\quad \quad}{for}\quad E_{1}} > {{\sum\limits_{n}\quad E_{n}}E_{\min}}} = {{0\quad {for}\quad E} \leq {\sum\limits_{n}\quad E_{n}}}}$

It can be seen that the minimum field value is taken with reference tothe first component field value since this is used as the phasereference.

As can be seen in step S9 it is determined whether the field value forthe phase reference, E₁, is less than or equal to the sum of theremaining fields and if so, in step S10 the minimum field value E_(min)is set to 0.

E_(min) is then compared with E_(limit) At Step S10 a and if E_(min) isgreater than or equal to then the probability of compliance is et tozero at step S10 b since the apparatus would be unable to fall withinthe EMI compliance value at the selected point.

In step S11 the range E_(max) to E_(min) is then divided into Mintervals and a count for each interval is set to zero. The upper limitto the ith interval is stored within E_(i). The count for the ithinterval is stored within C_(i). The process then enters a processingloop wherein step S12 the number of iterations S is set and a loopcounter s is set equal to 0 to initiate the loop. In step S13 the loopcounter s is incremented. In the first step in the processing loop arandom phase value for each phase-independent electric field component(ie for E₂ through to E_(n)) is generated (S14) and then thecorresponding peak amplitude of the combined field E_(c) is calculated(S15). The combined field E_(c) corresponding to this set of phasevalues is then calculated. The calculated combined field is theninterogated and the interval within which it falls is identified. Thecount for this interval is then incremented (S16). In step S17 it isthen determined whether the processing loop has completed the requirednumber of loops i.e. whether s=S and if not the process returns to stepS13 where the loop counter is incremented. In an embodiment, in order togenerate a significant statistical distribution, the loop is implemented50,000 times i.e. S=50,000.

In step S18 the probability density P(E_(i)) is calculated and in stepS19 the cumulative probability CP(E_(i))_(m) is calculated. Thecalculated cumulative probability is then compared with the thresholdfield defined by the EMC regulations to get the compliance probabilityin step S20 which is then output (S21).

At the point of leaving the processing loop (S17) a histogram of thenumber of peak amplitude of the combined field values that fall withinthe M discrete intervals between E_(min) and E_(max) is generated as arow of numbers. In step S18 the probability density is calculated using:${P\left( E_{i} \right)} = \frac{C_{i}}{S}$

FIG. 6 illustrates a calculated probability distribution. It can be seenthat if the threshold field set by the EMC regulations is 60 dBμV/m, thesystem is 100% compliant since there is no probability that the fieldcaused by emissions from the system can exceed the threshold fielddefined by the EMC regulations. If however, the EMC regulations definesa threshold field of 58 dBμV/m or less, there is a probability that thesystem will generate emissions sufficiently high enough to breach thisthreshold. The graph of FIG. 6 does not however, clearly identify whatthe likelihood of this occurring is.

In step S19 a cumulative probability is calculated using:$\left( {{CP}\left( E_{i} \right)} \right)_{m} = {\sum\limits_{i = 0}^{m}\quad {P\left( E_{i} \right)}}$

where E_(i) is the upper limit of the ith electric field component inthe distribution, and m is a number of the electric field component inthe distribution.

FIG. 7 illustrates the cumulative probability for the probabilitydistribution of FIG. 6. As can be seen the cumulative probabilityindicates the likelihood of the system complying with the EMCregulations depending upon the threshold set by the regulation. Forexample, if the threshold set by the regulation is 30 dBμV/m, there isalmost zero probability of the system complying. If the threshold is 60dBμV/m, there is a 100% probability of the system complying. For EMCregulations which defines the threshold between these field values, theprobability of compliance will depend upon the field threshold. Forexample, if the 80% rule is followed, as discussed hereinabove, thesystem would satisfy EMC regulations defining a threshold field of 53dBμV/m.

Thus using the cumulative probability as illustrated in FIG. 7 asderived using the method of FIG. 4, by comparing the values with thethreshold field of the EMC regulations, it is possible to generate aprobability which indicates the probability of the system complying withthe EMC regulations. This can be used to perform a risk analysis inorder to take a commercial decision.

The method of FIG. 5 can be carried out for a range of frequencies andfor a range of polarities such as vertically and horizontally in orderto ensure compliance with the EMC regulations over the range offrequencies as shown in FIG. 1. Thus, the graph can be plotted of thecompliance probability with respect to frequency. Further, as can beseen in FIG. 2, the compliance probability can be determined at avariety of analysis positions around the system 2 in order to provide amap of compliance probabilities at different positions and at differencedistances.

The present invention can be implemented as two procedures in softwareon a computer. The two procedures can comprise a compliance probabilitycalculation procedure and an interface procedure. The complianceprobability calculation procedure can carry out the steps of FIGS. 5aand 5 b. The interface procedure can provide a graphical interface tothe user to allow the user to view a layout of the equipment unitscomprising the system 2 and the compliance probabilities as illustratedin FIG. 2. Also, the compliance probability can be illustrated in thegraphical interface as a graph as shown in FIG. 7.

The apparatus for performing the method of FIGS. 5a and 5 b isillustrated in FIG. 8 and comprises an electromagnetic field data inputdevice 10 for receiving electromagnetic field data for each of thesources. An analysis point input device 11 allows a user to select theanalysis point and this is used in an electric field componentcalculator 12 to calculate the electric field component contribution atthe analysis point. The electromagnetic field data sorter 13 is providedto sort the electromagnetic field data into a descending order. Therandom number generator 14 generates a random number with equalprobability which is then used by the phase converter 15 to convert thisinto a phase between 0 and 2 π. The generated phases are then combinedwith the respective electromagnetic field data in the combiner 16 togenerate a combined electromagnetic field. The generated combinedelectric field is allocated to a particular memory location independence upon its value by the allocator 17 i.e. the histogram isbuilt up. The probability generator 18 calculates a probabilitydistribution using the histogram data and a cumulative probabilitygenerator 19 calculates the cumulative probability using the probabilitydistribution. An electromagnetic field limit data input device 21receives electromagnetic field limit data in dependence upon theelectromagnetic compatibility regulations and this is input togetherwith the cumulative probability into the compliance probabilitydeterminator 20 in order to determine a compliance probability.

FIG. 9 illustrates schematically apparatus for allowing a user to designa system to comply with the EMC regulations. A user interface isprovided and comprises a display device 30 and a user input andselection device 40. A compliance probability determinator unit 60 isprovided and comprises the apparatus of FIG. 8. Also a unit 50 fortranslating display arrangement of units into distance measurements isprovided. Thus the apparatus in FIG. 9 can be operated by a user to movesources S1 to S5 in FIG. 2, using the user selection device and in thisway selecting an appropriate arrangement of sources. The movement ofsources may be carried out automatically and iteratively from a startingarrangement e.g. a random arrangement. The user can input individualdata for each of the sources which can be used by the complianceprobability determinator unit. Also, the unit 50 can translate thedisplayed arrangement into distances which can be used by the complianceprobability determinator unit in order to determine the individualcontributions to the field caused by each of the sources at any numberof selected analysis points. In this way, the user is able to adapt thearrangement of equipment units within the system 2 in order to try toachieve the optimum arrangement for EMC compliance.

FIG. 10 illustrates a conventional computer 70 having a display device35 for displaying the layout of the units in the equipment 2 and fordisplaying the compliance probabilities. The user is able to interfaceto the device using the keyboard 41 and the pointing device 42. Thesystem can be implemented as a computer program provided on a magneticmedia such as a floppy disk 80.

It can be seen from the embodiments of the present invention describedhereinabove that the present invention provides a method of apparatusfor determining the likelihood that a system comprised of individualequipment units will comply with EMC regulations. Further, the presentinvention allows the user to design the layout of equipment units withinthe system optimally for EMC compliance.

Although the present invention has been described hereinabove withreference to specific embodiments it would be clear to a skilled personin the art that modifications are possible within the spirit and scopeof the present invention.

For the avoidance of doubt it is here noted that the system referred toin connection with the methods hereinbefore described may comprise asingle circuit board, the referenced plurality of equipment units beingthe component parts of such a circuit board including individual tracksthereon. Thus the invention may be applied equally to determining thelikelihood of an electric field at a position a distance from a printedcircuit board and caused by electromagnetic emissions from such acircuit board being less than or more than a predetermined electricfield where a plurality of components and/or printed circuit tracks ofthe circuit board individually radiate electromagnetic emissions.

It will also be noted that an equipment unit comprising a plurality ofprinted circuit boards may equally be considered as a system for thepurposes of electromagnetic emissions testing.

What is claimed is:
 1. A method of determining the likelihood of anelectric field strength at a position and caused by electromagneticemissions from a system at a distance from said position being less thanor more than a predefined electric field strength, where the systemcomprises a plurality of equipment units each of which individuallygenerates electromagnetic emissions, the method comprising: determiningthe individual electric field components at said position resulting fromradiated electromagnetic emissions from each said equipment unit;defining a threshold maximum electric field strength; summing therespective individual maximum electric field components to provide amaximum field strength value; determining whether said maximum fieldstrength value exceeds the threshold; summing the respective individualminimum electric field components to provide a minimum field strengthvalue if the maximum field strength value exceeds the threshold;determining whether said minimum field strength value exceeds thethreshold; and determining that the system cannot meet predefinedrequirements if the minimum field strength value exceeds the threshold,and otherwise, repeatedly assigning a random relative phase to theindividual electric field components, and calculating a compoundelectric field at said position using the determined electric fieldcomponents and said assigned phases to generate a distribution ofcompound electric field values; and statistically analysing saidgenerated distribution to determine the likelihood of the electric fieldat said position caused by said electromagnetic emissions being lessthan or more than said predefined electric field strength.
 2. A methodaccording to claim 1, wherein the statistical analysis step comprisesdetermining the cumulative probability for the compound electric fieldvalues, and determining if, for the predefined electric field, thecumulative probability is above or below the threshold.
 3. A methodaccording to claim 1, wherein the assigning step comprising assigning arelative phase randomly selected in accordance with a predefinedprobability distribution of possible relative phases.
 4. A methodaccording to claim 3, wherein each possible relative phase has equalprobability in the predefined probability distribution.
 5. A methodaccording to claim 1 wherein the determining step comprises calculatingthe individual electric field components based on known electromagneticemission properties of said equipment units and the distances from saidequipment units to said position.
 6. A method according to claim 5,wherein the known electromagnetic emission property for a said equipmentunit comprises a measured electric field at a distance from theequipment unit.
 7. A method according to claim 1 wherein said equipmentunits radiate electromagnetic emissions at a plurality of frequenciesand/or at horizontal and/or vertical polarities, and the method includesdetermining the likelihood for each frequency and/or polarity.
 8. Amethod according to claim 1 wherein said generated distributioncomprises a histogram of the number of calculated compound electricfield values that fall between a maximum possible compound electricfield and a minimum possible compound electric field.
 9. A methodaccording to claim 1 including determining the maximum possible compoundelectric field using the individual calculated electric fieldcomponents, wherein said repeated steps of assigning and calculating,and said statistical analysis step are only performed if the maximumpossible compound electric field is greater than said predefinedelectric field, and said likelihood is determined to be high if saidmaximum possible compound electric field is less than said predefinedelectric field.
 10. A method according to claim 1 including the steps ofperforming the method for a plurality of different said positions aroundsaid system to generate a map of likelihoods.
 11. A storage mediumstoring processor implementable instructions for controlling a processorto carry out the method of claim
 1. 12. An electronic signal carryingcomputer code for instructing a processor to carry out the method ofclaim
 1. 13. A method of designing a system equipment comprising aplurality of equipment units each of which individually radiateselectromagnetic emissions, the method comprising: arranging thepositions of said equipment units within a model of said system;determining the likelihood of an electric field at a position and causedby electromagnetic emissions from said system a distance from saidposition being less than or more than a predefined electric field usingthe method of claim 1; and rearranging the positions of said equipmentunits within said model of said system in dependence upon thedetermination and repeating the determining step.
 14. A method accordingto claim 13, wherein said determining step and the rearranging step arerepeated to achieve a higher likelihood of the electric field at saidposition being less than said predefined electric field.
 15. Apparatusfor determining the likelihood of an electric field strength at aposition and caused by electromagnetic emissions from a system at adistance from said position being less than zero more than a predefinedelectric field strength, where the system comprises a plurality ofequipment units each of which individually radiates electromagneticemissions, the apparatus comprising: determining means for determiningthe individual electric field components at said position resulting fromradiated electromagnetic emissions from each said equipment unit;defining means for defining a threshold maximum electric field strength;first calculating means for summing the respective individual maximumelectric field components to provide a maximum field strength value andfor summing the respective individual minimum electric field strengthcomponents to provide a minimum field strength value as needed;comparison means for comparing said maximum field strength value withthe threshold to determine whether said maximum field strength valueexceeds said threshold and if so, determining whether said minimum fieldstrength value exceeds the threshold and, if so, determining that thesystem cannot meet said predefined requirements and providing an outputthat indicates that the system cannot meet the predefined requirements;phase means for repeatedly assigning a random relative phase to theindividual electric field components; second calculating means forcalculating a compound electric field at said position using thedetermined electric field components and each repeatedly assigned phasefor each individual electric field component to generate a distributionof compound electric field values; and statistical analysis means forstatistically analysing said generated distribution to determine thelikelihood of the electric field at said position caused by saidelectromagnetic emissions being less than or more than said predefinedelectric field strength.
 16. Apparatus according to claim 15, whereinsaid statistical analysis means comprises means for determining thecumulative probability for the compound electric field values, and meansfor determining if, for the predefined electric, the cumulativeprobability is above or below a threshold.
 17. Apparatus according toclaim 15, wherein said phase means is adapted to assign a relative phaserandomly selected in accordance with a predefined probabilitydistribution of possible relative phases.
 18. Apparatus according toclaim 17, wherein said phase means is adapted to assign a relative phaserandomly selected in accordance with a probability distribution whereeach possible relative phase has equal probability.
 19. Apparatusaccording to claim 13, wherein said determining means is adapted tocalculated the individual electric field components based on knownelectromagnetic emission properties of said equipment units and thedistances from said equipment units to said position.
 20. Apparatusaccording to claim 19 wherein said determining means is adapted tocalculate the individual electric field components using the distancesfrom said equipment units to said position and a measured electric fieldfor each equipment unit at a distance from the equipment unit. 21.Apparatus according to claim 15, wherein said equipment units radiateelectromagnetic emissions at a plurality of frequencies and/or at aplurality of polarities, the apparatus being adapted to determine thelikelihood at each frequency and/or polarity.
 22. Apparatus according toclaim 15, wherein said second calculating means is adapted to generatesaid distribution as a histogram of the number of calculated compoundelectric field values that fall between a maximum possible compoundelectric field and a minimum possible compound electric field. 23.Apparatus according to claim 13, including means for calculating themaximum possible compound electric field using the individual determinedelectric field components; wherein said phase means, said calculatingmeans and said statistical analysis means are adapted to only beoperative if the maximum possible compound electric field is greaterthan said predefined electric field; and including means for determiningsaid likelihood to be high if said maximum possible compound electricfield is less than said predefined electric field.
 24. Apparatusaccording to claim 15, wherein said apparatus is adapted to perform thedetermination of said likelihood for a plurality of said positions, andincluding means for generating a map of said likelihoods for saidpositions around said system.
 25. Apparatus for designing a systemcomprising a plurality of equipment units each of which individuallyradiates electromagnetic emissions, the apparatus comprising: means forarranging the portion of said equipment units within a model of saidsystem; the apparatus of claim 15 for determining a likelihood of anelectric field at a position and caused by electromagnetic emissionsfrom said system a distance from said position being less than or morethan a predefined electric field; and means for rearranging the positionof said equipment units within said model of said system following theoperation of the determination apparatus, wherein the determiningapparatus is operable to redetermine said likelihood.